Introduction to Rational Functions

Christoph Schwarzweller

Formalized Mathematics (2012)

  • Volume: 20, Issue: 2, page 181-191
  • ISSN: 1426-2630

Abstract

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In this article we formalize rational functions as pairs of polynomials and define some basic notions including the degree and evaluation of rational functions [8]. The main goal of the article is to provide properties of rational functions necessary to prove a theorem on the stability of networks

How to cite

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Christoph Schwarzweller. "Introduction to Rational Functions." Formalized Mathematics 20.2 (2012): 181-191. <http://eudml.org/doc/267627>.

@article{ChristophSchwarzweller2012,
abstract = {In this article we formalize rational functions as pairs of polynomials and define some basic notions including the degree and evaluation of rational functions [8]. The main goal of the article is to provide properties of rational functions necessary to prove a theorem on the stability of networks},
author = {Christoph Schwarzweller},
journal = {Formalized Mathematics},
keywords = {degree and evaluation of rational functions; stability of networks},
language = {eng},
number = {2},
pages = {181-191},
title = {Introduction to Rational Functions},
url = {http://eudml.org/doc/267627},
volume = {20},
year = {2012},
}

TY - JOUR
AU - Christoph Schwarzweller
TI - Introduction to Rational Functions
JO - Formalized Mathematics
PY - 2012
VL - 20
IS - 2
SP - 181
EP - 191
AB - In this article we formalize rational functions as pairs of polynomials and define some basic notions including the degree and evaluation of rational functions [8]. The main goal of the article is to provide properties of rational functions necessary to prove a theorem on the stability of networks
LA - eng
KW - degree and evaluation of rational functions; stability of networks
UR - http://eudml.org/doc/267627
ER -

References

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  1. [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
  2. [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  3. [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
  4. [4] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  5. [5] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  6. [6] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. 
  7. [7] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. 
  8. [8] H. Heuser. Lehrbuch der Analysis. B.G. Teubner Stuttgart, 1990. 
  9. [9] Eugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990. 
  10. [10] Robert Milewski. The evaluation of polynomials. Formalized Mathematics, 9(2):391-395, 2001. 
  11. [11] Robert Milewski. Fundamental theorem of algebra. Formalized Mathematics, 9(3):461-470, 2001. 
  12. [12] Robert Milewski. The ring of polynomials. Formalized Mathematics, 9(2):339-346, 2001. 
  13. [13] Michał Muzalewski. Construction of rings and left-, right-, and bi-modules over a ring. Formalized Mathematics, 2(1):3-11, 1991. 
  14. [14] Michał Muzalewski and Lesław W. Szczerba. Construction of finite sequences over ring and left-, right-, and bi-modules over a ring. Formalized Mathematics, 2(1):97-104, 1991. 
  15. [15] Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991. 
  16. [16] Christoph Schwarzweller and Agnieszka Rowinska-Schwarzweller. Schur’s theorem on the stability of networks. Formalized Mathematics, 14(4):135-142, 2006, doi:10.2478/v10037-006-0017-9.[Crossref] 
  17. [17] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990. 
  18. [18] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990. 
  19. [19] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990. 
  20. [20] Wojciech A. Trybulec. Lattice of subgroups of a group. Frattini subgroup. FormalizedMathematics, 2(1):41-47, 1991. 
  21. [21] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  22. [22] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990. 
  23. [23] Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992. 

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